<PAGE>

                                                                     EXHIBIT 4.2

             AMENDMENT TO STOCKHOLDER PROTECTION RIGHTS AGREEMENT

          AMENDMENT (the "Amendment"), dated as of March 27, 2001, to the
Stockholder Protection Rights Agreement, dated as of January 16, 1996 (the
"Rights Agreement"), between New York Community Bancorp, Inc., a Delaware
corporation (the "Company"), and Mellon Investor Services LLC (formerly known as
Chemical Mellon Shareholder Services, L.L.C.), as Rights Agent (the "Rights
Agent").

                                   RECITALS

          WHEREAS, the Company and the Rights Agent have heretofore executed and
entered into the Rights Agreement.

          WHEREAS, Richmond County Financial Corp., a Delaware corporation
("RCF") and the Company contemplate entering into an Agreement and Plan of
Merger (the "Plan") pursuant to which RCF will merge with and into the Company
(the "Merger"). The Board of Directors of the Company has approved the Plan.

          WHEREAS, in connection with the Plan, RCF and the Company contemplate
entering into a stock option agreement (the "East Stock Option Agreement")
pursuant to which the Company will grant to RCF an option to purchase shares of
the Company's common stock, par value $0.01 per share, on the terms and subject
to the conditions set forth in the East Stock Option Agreement. The Board of
Directors of the Company has approved the East Stock Option Agreement.

          WHEREAS, pursuant to Section 5.4 of the Rights Agreement, the Company
and the Rights Agent may from time to time supplement and amend the Rights
Agreement.

          WHEREAS, the Board of Directors of the Company has determined that an
amendment to the Rights Agreement as set forth herein is necessary and desirable
in connection with the foregoing and the Company and the Rights Agent desire to
evidence such amendment in writing.

          WHEREAS, all acts and things necessary to make this Amendment a valid
agreement, enforceable according to its terms have been done and performed, and
the execution and delivery of this Amendment by the Company and the Rights Agent
have been in all respects duly authorized by the Company and the Rights Agent.
<PAGE>

          Accordingly, the parties agree as follows:

          A. Amendment of Section 1.1. Section 1.1 of the Rights Agreement is
             ------------------------
supplemented to add the following definitions in the appropriate locations:

          "RCF" means Richmond County Financial Corp., a Delaware corporation.

          "Merger" shall have the meaning set forth in the Plan.

          "Plan" shall mean the Agreement and Plan of Merger, dated as of March
27, 2001, by and between the Company and RCF, as it may be amended from time to
time.

          "East Stock Option Agreement" shall have the meaning set forth in the
Plan.

          B. Amendment of the definition of "Acquiring Person". The definition
             -------------------------------------------------
of "Acquiring Person" in Section 1.1 of the Rights Agreement is amended by
adding the following sentence at the end thereof:

          "Notwithstanding anything in this Rights Agreement to the contrary,
     RCF shall not be deemed to be an Acquiring Person solely by virtue of (i)
     the execution of the Plan or the East Stock Option Agreement, (ii) the
     consummation of the Merger or (iii) the consummation of any other
     transaction contemplated in the Plan or the East Stock Option Agreement."

          C. Amendment of the definition of "Stock Acquisition Date". The
             -------------------------------------------------------
definition of "Stock Acquisition Date" in Section 1.1 of the Rights Agreement is
amended by adding the following sentence at the end thereof:

          "Notwithstanding anything in this Rights Agreement to the contrary, a
Stock Acquisition Date shall not be deemed to have occurred solely as the result
of (i) the execution of the Plan or the East Stock Option Agreement, (ii) the
consummation of the Merger, or (iii) the consummation of any other transaction
contemplated in the Plan or the East Stock Option Agreement."

          D. Amendment of definition of "Flip-in Date". The definition of
             -----------------------------------------
"Flip-in Date" in Section 1.1 of the Rights Agreement is amended by adding the
following sentence at the end thereof:

          "Notwithstanding anything in this Rights Agreement to the contrary, a
     Flip-in Date shall not be deemed to have occurred solely as the result of
     (i) the execution of the Plan or the East Stock Option Agreement, (ii) the
     consummation of the Merger, or

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<PAGE>

     (iii) the consummation of any other transaction contemplated in the Plan or
     the East Stock Option Agreement."

          F. Amendment of Section 2.3. Section 2.3 of the Rights Agreement is
             ------------------------
amended to add the following sentence at the end thereof as Section 2.3(h):

          "Nothing in this Rights Agreement shall be construed to give any
     holder of Rights or any other Person any legal or equitable rights,
     remedies or claims under this Rights Agreement by virtue of the execution
     of the Plan or the East Stock Option Agreement or by virtue of any of the
     transactions contemplated by the Plan Agreement or the East Stock Option
     Agreement."

          G. Amendment of Section 4.3(c). Section 4.3(c) of the Rights Agreement
             ---------------------------
is amended to add the following sentence at the end thereof:

          "Anything to the contrary notwithstanding, in no event shall the
     Rights Agent be liable for special, punitive, indirect, consequential or
     incidental loss or damage of any kind whatsoever (including but not limited
     to lost profits), even if the Rights Agent has been advised of the
     likelihood of such loss or damage.

          H. Effectiveness. This Amendment shall be deemed effective as of the
             -------------
date first written above, as if executed on such date. Except as amended hereby,
the Rights Agreement shall remain in full force and effect and shall be
otherwise unaffected hereby.

          I. Miscellaneous. This Amendment shall be deemed to be a contract made
             -------------
under the laws of the State of Delaware and for all purposes shall be governed
by and construed in accordance with the laws of such state applicable to
contracts to be made and performed entirely within such state. This Amendment
may be executed in any number of counterparts, each of such counterparts shall
for all purposes be deemed to be an original, and all such counterparts shall
together constitute but one and the same instrument. If any provision, covenant
or restriction of this Amendment is held by a court of competent jurisdiction or
other authority to be invalid, illegal or unenforceable, the remainder of the
terms, provisions, covenants and restrictions of this Amendment shall remain in
full force and effect and shall in no way be effected, impaired or invalidated.

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<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be duly executed and attested, all as of the date and year first above written.

Attest:                                     NEW YORK COMMUNITY BANCORP, INC.

By: /s/ Michael J. Lincks                   By: /s/ Joseph R. Ficalora
    --------------------------                  -------------------------------
    Name:  Michael J. Lincks                    Name:  Joseph R. Ficalora
    Title: Executive Vice President             Title: Chairman, Chief Executive
           and Corporate Secretary                     Officer and President

Attest:                                     MELLON INVESTOR SERVICES LLC

By: /s/ James Hagan                         By: /s/ Kirk Alexander
    --------------------------                  -------------------------------
    Name:  James Hagan                          Name:  Kirk Alexander
    Title: Vice President                       Title: Relationship Manager




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